27 research outputs found
Fundamental Limits to Position Determination by Concentration Gradients
Position determination in biological systems is often achieved through
protein concentration gradients. Measuring the local concentration of such a
protein with a spatially-varying distribution allows the measurement of
position within the system. In order for these systems to work effectively,
position determination must be robust to noise. Here, we calculate fundamental
limits to the precision of position determination by concentration gradients
due to unavoidable biochemical noise perturbing the gradients. We focus on
gradient proteins with first order reaction kinetics. Systems of this type have
been experimentally characterised in both developmental and cell biology
settings. For a single gradient we show that, through time-averaging, great
precision can potentially be achieved even with very low protein copy numbers.
As a second example, we investigate the ability of a system with oppositely
directed gradients to find its centre. With this mechanism, positional
precision close to the centre improves more slowly with increasing averaging
time, and so longer averaging times or higher copy numbers are required for
high precision. For both single and double gradients, we demonstrate the
existence of optimal length scales for the gradients, where precision is
maximized, as well as analyzing how precision depends on the size of the
concentration measuring apparatus. Our results provide fundamental constraints
on the positional precision supplied by concentration gradients in various
contexts, including both in developmental biology and also within a single
cell.Comment: 24 pages, 2 figure
Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis
We analyse the efficiency of several simulation methods which we have
recently proposed for calculating rate constants for rare events in stochastic
dynamical systems, in or out of equilibrium. We derive analytical expressions
for the computational cost of using these methods, and for the statistical
error in the final estimate of the rate constant, for a given computational
cost. These expressions can be used to determine which method to use for a
given problem, to optimize the choice of parameters, and to evaluate the
significance of the results obtained. We apply the expressions to the
two-dimensional non-equilibrium rare event problem proposed by Maier and Stein.
For this problem, our analysis gives accurate quantitative predictions for the
computational efficiency of the three methods.Comment: 19 pages, 13 figure
Hydrophobic interactions: an overview
We present an overview of the recent progress that has been made in
understanding the origin of hydrophobic interactions. We discuss the different
character of the solvation behavior of apolar solutes at small and large length
scales. We emphasize that the crossover in the solvation behavior arises from a
collective effect, which means that implicit solvent models should be used with
care. We then discuss a recently developed explicit solvent model, in which the
solvent is not described at the atomic level, but rather at the level of a
density field. The model is based upon a lattice-gas model, which describes
density fluctuations in the solvent at large length scales, and a Gaussian
model, which describes density fluctuations at smaller length scales. By
integrating out the small length scale field, a Hamiltonian is obtained, which
is a function of the binary, large-length scale field only. This makes it
possible to simulate much larger systems than hitherto possible as demonstrated
by the application of the model to the collapse of an ideal hydrophobic
polymer. The results show that the collapse is dominated by the dynamics of the
solvent, in particular the formation of a vapor bubble of critical size.
Implications of these findings to the understanding of pressure denaturation of
proteins are discussed.Comment: 10 pages, 4 figure
Computing stationary distributions in equilibrium and non-equilibrium systems with Forward Flux Sampling
We present a method for computing stationary distributions for activated
processes in equilibrium and non-equilibrium systems using Forward Flux
Sampling (FFS). In this method, the stationary distributions are obtained
directly from the rate constant calculations for the forward and backward
reactions; there is no need to perform separate calculations for the stationary
distribution and the rate constant. We apply the method to the non-equilibrium
rare event problem proposed by Maier and Stein, to nucleation in a
2-dimensional Ising system, and to the flipping of a genetic switch
Forward Flux Sampling for rare event simulations
Rare events are ubiquitous in many different fields, yet they are notoriously
difficult to simulate because few, if any, events are observed in a conventiona
l simulation run. Over the past several decades, specialised simulation methods
have been developed to overcome this problem. We review one recently-developed
class of such methods, known as Forward Flux Sampling. Forward Flux Sampling
uses a series of interfaces between the initial and final states to calculate
rate constants and generate transition paths, for rare events in equilibrium or
nonequilibrium systems with stochastic dynamics. This review draws together a
number of recent advances, summarizes several applications of the method and
highlights challenges that remain to be overcome.Comment: minor typos in the manuscript. J.Phys.:Condensed Matter (accepted for
publication
Generic mechanism for generating a liquid-liquid phase transition
Recent experimental results indicate that phosphorus, a single-component
system, can have two liquid phases: a high-density liquid (HDL) and a
low-density liquid (LDL) phase. A first-order transition between two liquids of
different densities is consistent with experimental data for a variety of
materials, including single-component systems such as water, silica and carbon.
Molecular dynamics simulations of very specific models for supercooled water,
liquid carbon and supercooled silica, predict a LDL-HDL critical point, but a
coherent and general interpretation of the LDL-HDL transition is lacking. Here
we show that the presence of a LDL and a HDL can be directly related to an
interaction potential with an attractive part and two characteristic
short-range repulsive distances. This kind of interaction is common to other
single-component materials in the liquid state (in particular liquid metals),
and such potentials are often used to decribe systems that exhibit a density
anomaly. However, our results show that the LDL and HDL phases can occur in
systems with no density anomaly. Our results therefore present an experimental
challenge to uncover a liquid-liquid transition in systems like liquid metals,
regardless of the presence of the density anomaly.Comment: 5 pages, 3 ps Fig
Measuring every particle's size from three-dimensional imaging experiments
Often experimentalists study colloidal suspensions that are nominally
monodisperse. In reality these samples have a polydispersity of 4-10%. At the
level of an individual particle, the consequences of this polydispersity are
unknown as it is difficult to measure an individual particle size from
microscopy. We propose a general method to estimate individual particle radii
within a moderately concentrated colloidal suspension observed with confocal
microscopy. We confirm the validity of our method by numerical simulations of
four major systems: random close packing, colloidal gels, nominally
monodisperse dense samples, and nominally binary dense samples. We then apply
our method to experimental data, and demonstrate the utility of this method
with results from four case studies. In the first, we demonstrate that we can
recover the full particle size distribution {\it in situ}. In the second, we
show that accounting for particle size leads to more accurate structural
information in a random close packed sample. In the third, we show that crystal
nucleation occurs in locally monodisperse regions. In the fourth, we show that
particle mobility in a dense sample is correlated to the local volume fraction.Comment: 7 pages, 5 figure
Regulatory control and the costs and benefits of biochemical noise
Experiments in recent years have vividly demonstrated that gene expression
can be highly stochastic. How protein concentration fluctuations affect the
growth rate of a population of cells, is, however, a wide open question. We
present a mathematical model that makes it possible to quantify the effect of
protein concentration fluctuations on the growth rate of a population of
genetically identical cells. The model predicts that the population's growth
rate depends on how the growth rate of a single cell varies with protein
concentration, the variance of the protein concentration fluctuations, and the
correlation time of these fluctuations. The model also predicts that when the
average concentration of a protein is close to the value that maximizes the
growth rate, fluctuations in its concentration always reduce the growth rate.
However, when the average protein concentration deviates sufficiently from the
optimal level, fluctuations can enhance the growth rate of the population, even
when the growth rate of a cell depends linearly on the protein concentration.
The model also shows that the ensemble or population average of a quantity,
such as the average protein expression level or its variance, is in general not
equal to its time average as obtained from tracing a single cell and its
descendants. We apply our model to perform a cost-benefit analysis of gene
regulatory control. Our analysis predicts that the optimal expression level of
a gene regulatory protein is determined by the trade-off between the cost of
synthesizing the regulatory protein and the benefit of minimizing the
fluctuations in the expression of its target gene. We discuss possible
experiments that could test our predictions.Comment: Revised manuscript;35 pages, 4 figures, REVTeX4; to appear in PLoS
Computational Biolog
Transcriptional Regulation by Competing Transcription Factor Modules
Gene regulatory networks lie at the heart of cellular computation. In these networks, intracellular and extracellular signals are integrated by transcription factors, which control the expression of transcription units by binding to cis-regulatory regions on the DNA. The designs of both eukaryotic and prokaryotic cis-regulatory regions are usually highly complex. They frequently consist of both repetitive and overlapping transcription factor binding sites. To unravel the design principles of these promoter architectures, we have designed in silico prokaryotic transcriptional logic gates with predefined input–output relations using an evolutionary algorithm. The resulting cis-regulatory designs are often composed of modules that consist of tandem arrays of binding sites to which the transcription factors bind cooperatively. Moreover, these modules often overlap with each other, leading to competition between them. Our analysis thus identifies a new signal integration motif that is based upon the interplay between intramodular cooperativity and intermodular competition. We show that this signal integration mechanism drastically enhances the capacity of cis-regulatory domains to integrate signals. Our results provide a possible explanation for the complexity of promoter architectures and could be used for the rational design of synthetic gene circuits
Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly
We investigate the phase behavior of a single-component system in 3
dimensions with spherically-symmetric, pairwise-additive, soft-core
interactions with an attractive well at a long distance, a repulsive soft-core
shoulder at an intermediate distance, and a hard-core repulsion at a short
distance, similar to potentials used to describe liquid systems such as
colloids, protein solutions, or liquid metals. We showed [Nature {\bf 409}, 692
(2001)] that, even with no evidences of the density anomaly, the phase diagram
has two first-order fluid-fluid phase transitions, one ending in a
gas--low-density liquid (LDL) critical point, and the other in a
gas--high-density liquid (HDL) critical point, with a LDL-HDL phase transition
at low temperatures. Here we use integral equation calculations to explore the
3-parameter space of the soft-core potential and we perform molecular dynamics
simulations in the interesting region of parameters. For the equilibrium phase
diagram we analyze the structure of the crystal phase and find that, within the
considered range of densities, the structure is independent of the density.
Then, we analyze in detail the fluid metastable phases and, by explicit
thermodynamic calculation in the supercooled phase, we show the absence of the
density anomaly. We suggest that this absence is related to the presence of
only one stable crystal structure.Comment: 15 pages, 21 figure